Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 24 - The Wave Nature of Light - General Problems - Page 711: 84

Answer

$240\;\rm nm$

Work Step by Step

As we see in the figure below, the two reflected rays experience a $\pi$ phase change due to reflection from a medium with a greater index of refraction. For constructive interference from the film when the two rays are reflected in phase, the path length difference is given by $$2t=m\lambda_n=\dfrac{m\lambda}{n_{coating}}$$ And hence the thickness of the film is given by $$t=\dfrac{m\lambda}{2n_{coating}}$$ At $m=0$, the thickness will be zero which means there is no coating at all. So, we can work with $m=1$ for the minimum thickness needed. $$t=\dfrac{ \lambda}{2n_{coating}}$$ For red light; $$t=\dfrac{ 643}{2\cdot 1.34}=\color{red}{\bf 240}\;\rm nm$$
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